Tens of millions of seniors rely on Medicare for their health-related needs in retirement. But while the public insurance program has many benefits, the fact remains that it doesn't cover a number of health services that all seniors need. As such, they are often left with no choice but to cover those services completely out of pocket, which can be a strain on their financial resources. Here are three common expenses that Medicare won't pick up the tab for.

1. Dental care

Maintaining proper oral health is critical for seniors, so it's somewhat surprising that Medicare won't pay for things like dental cleanings, fillings, and dentures. It also won't cover most oral or gum surgeries. The only exception is for patients who need these exams or surgeries in conjunction with another medical procedure or issue. For example, if you need an oral exam prior to a transplant, Medicare will generally cover it. Otherwise, you're out of luck.

The word Medicare spelled out in round beads

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That said, seniors do have options for securing dental coverage. First, you can buy dental insurance on your own, though the price of a plan might be such that you'd be better off just paying for your dental care out of pocket. You can also look at getting a Medicare Advantage plan. Also called Medicare Part C, these private plans are designed to supplement original Medicare (Parts A and B), and thus cover many of the services it does not. Finally, if you happen to live within reach of one of the nation's 66 dental schools, don't write off the idea of seeking treatment there. Their students treat patients at a substantial discount, and they are always monitored by faculty, so you shouldn't worry about the quality of care -- although procedures can take longer than they might at a regular dentist's office.

2. Hearing aids

Many of us will suffer significant hearing loss as we age, but once again, Medicare comes up short on the coverage front. And that's unfortunate, because the average cost of a digital hearing device and its associated fittings can range from $1,500 all the way up to $5,000, according to the National Institutes of Health.

The good news? Medicare Advantage generally covers hearing services, so if you opt for one of these supplemental plans, that's one less completely out-of-pocket expense to worry about.

3. Vision services

Regular eye checkups are crucial for seniors, since untreated issues can result in permanent damage. Furthermore, a large chunk of the U.S. population, seniors included, relies on eyeglasses to see and function.

Unfortunately, Medicare doesn't pay for either eyeglasses or vision exams, though it generally will pay for eye care treatment that is medical in nature. For example, if you sustain an eye injury during a fall, Medicare will generally cover the related health care costs. Similarly, it will pay for certain tests or treatments related to eye disease.

Furthermore, Medicare will pay for annual eye exams for diabetic retinopathy for those who have been diagnosed with diabetes. And, it will cover annual glaucoma tests for those deemed to be at high risk for the disease.

If you enroll in a Medicare Advantage plan, you'll generally have your vision needs covered. Otherwise, if you have a membership to a  warehouse club, consider getting your glasses there, as you'll likely score a much lower price than you'd find at an optician's office. There are also a number of online outlets, like Warby Parker, that let you buy glasses on the cheap. The only catch is that you need a valid prescription, and again, that's not something original Medicare will pay for.

Many retirees find that healthcare is their single greatest monthly expense. Knowing what Medicare does and does not pay for will help you budget properly for that period of your life.